发表机构
ETH Zürich; University of Maryland, College Park（苏黎世联邦理工学院; 马里兰大学帕克分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将条件流匹配（CFM）集成至EngiOpt，在EngiBench的两项基准任务上对比条件扩散模型与cGAN，结果显示CFM的性能更优、采样速率更高且所需网络评估次数更少。
AI 中文摘要
工程逆设计常受限于偏微分方程（PDE）约束优化问题迭代求解器的高计算成本及其对初始化的敏感性。深度生成模型可在推理时无需重运行模拟器即可生成候选设计：生成对抗网络（GAN）通过一次前向传播采样，而扩散模型则需迭代的逆时间积分。本研究将条件流匹配（CFM）集成至EngiOpt中，并在EngiBench的结构（beams2d）和热传导（heatconduction2d）基准上，采用相同的下游优化协议，将其与条件扩散模型、条件生成对抗网络（cGAN）进行对比。采用累积最优间隙（COG）和最终最优间隙（FOG）作为核心指标，评估生成设计作为基于梯度优化的初始解的性能。在评估的EngiOpt实现及两项EngiBench任务中，CFM在两项任务上均实现了最低的COG、FOG、最大均值差异（MMD）及体积分数偏差；CFM在beams2d和heatconduction2d上的平均体积分数偏差分别为0.4%和1.0%，而扩散模型分别为3.8%和11.2%。在欧拉s=16时，CFM在beams2d上的采样速率为53.2样本/秒，约为相同时序协议下使用1000次网络评估的扩散基线吞吐量的66倍，其COG为1.182±3.126，而欧拉s=32时的COG为1.173±3.100。在两项任务中，CFM生成的初始解的COG均低于两个基线模型，且所需网络评估次数少于扩散模型。
英文摘要
Engineering inverse design is often limited by the high computational cost of iterative solvers for optimization problems constrained by partial differential equations (PDEs) and by their sensitivity to initialization. Deep generative models can produce candidate designs without rerunning the simulator at inference time. Generative adversarial networks (GANs) sample in one forward pass, whereas diffusion models require iterative reverse-time integration. In this work, we add conditional flow matching (CFM) to EngiOpt and compare it with a conditional diffusion model and a conditional generative adversarial network (cGAN) on structural (beams2d) and thermal (heatconduction2d) benchmarks from EngiBench using the same downstream optimization protocol. We use cumulative optimality gap (COG) and final optimality gap (FOG) as the primary metrics for evaluating the generated designs as warm starts for gradient-based refinement. On the evaluated EngiOpt implementations and two EngiBench tasks, CFM achieves the lowest measured COG, FOG, maximum mean discrepancy (MMD), and volume-fraction deviation on both tasks. CFM has mean volume-fraction deviations of 0.4% and 1.0% on beams2d and heatconduction2d, respectively, compared with 3.8% and 11.2% for diffusion. At Euler s = 16, CFM achieves 53.2 samples/s on beams2d, about 66 times the measured throughput of the evaluated diffusion baseline using 1000 network evaluations under the same timing protocol, with COG 1.182 +/- 3.126, compared with 1.173 +/- 3.100 for Euler s = 32. Across the two tasks, CFM produces warm starts with lower measured COG than both baselines and uses fewer network evaluations than diffusion.
Comments13 pages, 2 figures, 6 tables. Accepted for presentation at EngOpt 2026
